Lena Schend

Challenges to complexity shields that are supposed to protect elections against manipulation and control: a survey

In the context of voting, manipulation and control refer to attempts to influence the outcome of elections by either setting some of the votes strategically (i.e., by reporting untruthful preferences) or by altering the structure of elections via adding, deleting, or partitioning either candidates or voters. Since by the celebrated Gibbard–Satterthwaite theorem (and other results expanding its scope) all reasonable voting systems are manipulable in principle and since many voting systems are in principle susceptible to many control types modeling natural control scenarios, much work has been done to use computational complexity as a shield to protect elections against manipulation and control. However, most of this work has merely yielded NP-hardness results, showing that certain voting systems resist certain types of manipulation or control only in the worst case. Various approaches, including studies of the typical case (where votes are given according to some natural distribution), pose serious challenges to such worst-case complexity results and might allow successful manipulation or control attempts, despite the NP-hardness of the corresponding problems. We survey and discuss some recent results on these challenges to complexity results for manipulation and control, including typical-case analyses and experiments, fixed-parameter tractability, domain restrictions (single-peakedness), and approximability.

Control complexity in Bucklin and fallback voting: A theoretical analysis

Electoral control models ways of changing the outcome of an election via such actions as adding, deleting, or partitioning either candidates or voters. To protect elections from such control attempts, computational complexity has been used to establish so-called resistance results. We show that fallback voting, an election system proposed by Brams and Sanver [12] to combine Bucklin with approval voting, displays the broadest control resistance currently known to hold among natural election systems with a polynomial-time winner problem. We also study the control complexity of Bucklin voting and show that it performs almost as well as fallback voting in terms of control resistance. Furthermore, we investigate the parameterized control complexity of Bucklin and fallback voting, according to several parameters that are often likely to be small for typical instances. In a companion paper [28], we challenge our worst-case complexity results from an experimental point of view.

Complexity of manipulation, bribery, and campaign management in Bucklin and fallback voting

A central theme in computational social choice is to study the extent to which voting systems computationally resist manipulative attacks seeking to influence the outcome of elections, such as manipulation (i.e., strategic voting), control, and bribery. Bucklin and fallback voting are among the voting systems with the broadest resistance (i.e., NP-hardness) to control attacks. However, only little is known about their behavior regarding manipulation and bribery attacks. We comprehensively investigate the computational resistance of Bucklin and fallback voting for many of the common manipulation and bribery scenarios; we also complement our discussion by considering several campaign-management problems for these two voting rules.

Control complexity in Bucklin and fallback voting: An experimental analysis☆

Control in elections models situations in which an external actor tries to change the outcome of an election by restructuring the election itself. The corresponding decision problems have been shown NP-hard for a variety of voting systems. In particular, in our companion paper [16], we have shown that fallback and Bucklin voting are resistant (in terms of NP-hardness) to almost all of the common types of control. While NP-hardness results for manipulation (another way of tampering with the outcomes of elections) have been challenged experimentally (see, e.g., the work of Walsh [38] and [37]), such an experimental approach is sorely missing for control. We for the first time tackle NP-hard control problems in an experimental setting. Our experiments allow a more fine-grained analysis and comparison—across various control scenarios, vote distribution models, and voting systems—than merely stating NP-hardness for all these control problems.

Toward the complexity of the existence of wonderfully stable partitions and strictly core stable coalition structures in enemy-oriented hedonic games

We study the computational complexity of the existence and the verification problem for wonderfully stable partitions (WSPE and WSPV) and of the existence problem for strictly core stable coalition structures (SCSCS) in enemy-oriented hedonic games. In this note, we show that WSPV is NP-complete and both WSPE and SCSCS are DP-hard, where DP is the second level of the boolean hierarchy, and we discuss an approach for classifying the latter two problems in terms of their complexity.

Borda-induced hedonic games with friends, enemies, and neutral players

Abstract In a FEN-hedonic game, each player partitions the set of other players into friends, enemies, and neutral players and ranks her friends and enemies. Assuming that preferences are monotonic with respect to adding friends and antimonotonic with respect to adding enemies, we use bipolar responsive extensions to lift the players’ rankings of players to their (partial) preferences over coalitions. We propose cardinal comparability functions in order to extend partial to complete preference orders consistent with these polarized responsive orders, in particular focusing on Borda-induced FEN-hedonic games. For a number of common solution concepts, we study the computational complexity of the existence and the verification problem.